Our Prius was involved in a collision (everyone is safe) and we didn't drive the car for a couple months while it was being repaired. It seems to me that BA (before accident) the radio always stayed on after you turned off the car, but it would stop playing when you opened the door. Is that my imagination? Well... the radio turns off when the car is turned off and I don't think it was like that BA.
I have a 2010 G3. One of my many complaints about the electronics in this car is that it has retained power for the windows, but not the radio. I'm thinking that yours might have been the same BA. Good Luck.
Ours too: car off means radio's off. If you really wanted to hear the end of that song, you need to give the start button a push with foot off the brake. First car we've ever had that behaves like that. Considering the 12 volt battery capacity, probably a good idea.